Microeconomia 2/ed
David A. Besanko, Ronald R. Braeutigam
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CHAPTER 3
© 2012 The McGraw-Hill Companies srl
CONSUMER PREFERENCES AND THE CONCEPT OF UTILITY
rather than diminishing. Sometimes a consumer may simply be unwilling to substitute
one commodity for another. For example, a consumer might always want exactly
1 ounce of peanut butter for each ounce of jelly on his sandwiches and be unwilling to
consume peanut butter and jelly in any other proportions. To cover cases such as these
and others, there are several special utility functions. Here we discuss four: utility
functions in the case of perfect substitutes and the case of perfect complements, the
Cobb–Douglas utility function, and quasi-linear utility functions.
Perfect Substitutes
perfect substitutes (in
consumption) Two goods
such that the marginal rate of
substitution of one good for
the other is constant; therefore, the indifference curves
are straight lines.
In some cases, a consumer might view two commodities as perfect substitutes for one
another. Two goods are perfect substitutes when the marginal rate of substitution
of one for the other is a constant. For example, suppose David likes both butter (B)
and margarine (M) and that he is always willing to substitute a pound of either
commodity for a pound of the other. Then MRSB, M = MRSM, B = 1. We can use a
utility function such as U = aB + aM, where a is any positive constant, to describe
these preferences. (With this utility function, MUB = a and MUM = a . It also follows
that MRSB, M = MUB /MUM = a/a = 1, and the slope of the indifference curves will
be constant and equal to −1.)
More generally, indifference curves for perfect substitutes are straight lines, and
the marginal rate of substitution is constant, though not necessarily equal to 1. For
example, suppose a consumer likes both pancakes and waffles and is always willing to
substitute two pancakes for one waffle. A utility function that would describe his
preferences is U = P + 2W, where P is the number of pancakes and W the number
of waffles. With these preferences, MUP = 1 and MUW = 2, so each waffle
A P P L I C A T I O N
3.3
Taste Tests
If you listen to advertisements on television, you might
believe that beer is a highly differentiated product and
that most consumers have strong preferences for one
beer over another. To be sure, there are differences
among beers, and not all brands are sold at the same
price. But are brands so different that one brewer could
raise the price of its product without losing a significant
portion of its sales?
In looking at the U.S. beer industry, Kenneth Elzinga
observed, “Several studies indicate that, at least under
blindfold test conditions, most beer drinkers cannot distinguish between brands of beer.” He also noted that brewers have devoted “considerable talent and resources . . . to
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publicizing real or imagined differences in beers, with the
hope of producing product differentiation.” In the end,
Elzinga suggested, despite brewers’ efforts to differentiate their products from those of their competitors, most
consumers would be quite willing to substitute one
brand of beer for another, especially if one brand were
to raise its price significantly.10
Elzinga’s analysis does not suggest that all
consumers regard brands of beer as perfect substitutes.
However, when a consumer does not have a strong
preference for one beer over another, then the
marginal rate of substitution of brand A for brand B
might be nearly constant, and probably near 1, since a
consumer would probably be willing to give up one
glass of brand A for one glass of brand B.
K. Elzinga, “The Beer Industry,” in W. Adams, The Structure of American Industry, 8th ed. (New York:
Macmillan Publishing Company, 1990).